We assume that the initial states of the system and environment are separable, i.e., \(\rho _{S R}^{I}(0)=\rho _{S}(0) \otimes \rho _{R}(0)\) . In the Born-Markov approximaton, we obtain the following master equation for the system [1]}, [2]}
\(\begin{aligned}\dot{\rho }_{S}(t)=& -\frac{i}{\hbar }\left[\hat{H}_{S}(\vec{k}), \rho _{S}\right]+\mathcal {U}(\rho _S)+\mathcal {D}(\rho _S),\end{aligned}\) 
